Feedback of channel stat information (CSI) can increase the performance of closed-loop (CL) multiple-input, multiple-output (MIMO) wireless networks. In MIMO networks, each cell includes a base station (BS) and a set of mobile stations (MS), where each MS estimates and feeds back the CSI of a downlink (DL) from the BS to the MS on an uplink (UL). The feedback can either be codebook based, or in analog form. The CSI feedback is particularly important for the MS at edges of adjacent cells where inter-cell interference (ICI) can occur. As defined herein, feeding back means transmitting from the MS to the BS.
Feeding back rank adapted channel singular vectors, in a similar fashion to codebook based feedback, is superior to all other analog feedback forms known for single-user (SU) MIMO networks.
Feedback in analog form mitigates colored interference regardless of channel conditions, signal-to-noise ratios (SNR) and interference color, when compared to codebook based feedback when both use the UL channel resources.
In addition to pure analog feedback options, one can also use analog feedback for a differential mode. The difference is between the optimal singular vector and the best codeword that is fed back unquantized.
The main appeal of analog feedback is for multi user MIMO (MU-MIMO) applications, or multi-BS MIMO applications, including femto and relay networks, where joint processing of multiple BS is performed to achieve coherent combining and interference nulling for MS at the edges of the adjacent cells.
This is mainly due to the fact that the channel feedback accuracy must increase linearly in dB with an increase in the SNR to remain within fixed amount of dB from the MU-MIMO channel capacity.
Analog feedback is best suited for this task. The accuracy naturally increases with the SNR, and can provide simple and unified feedback for a typical macro-cell, as well as femto and pico cells, and relay station to base station links, where the typical SNR is expected to be much higher.
On the other hand, codebook feedback in networks designed according to the IEEE 802.16m standard limits the performance, due to channel feedback quantization errors at the MS.
The current IEEE 802.16m “System Description Document” (SDD) assumes rank-1 feedback for MU-MIMO. Therefore, it is desired to optimize analog feedback by informing the transmitter with a largest singular vector. As defined herein, the largest singular vector is the vector associated with the singular value with maximum magnitude.
General Analog Rank-1 Feedback
As shown in FIG. 1, for a conventional BS with N antennas, N complex valued numbers are needed to represent the largest singular vector of the transmit covariance matrix. Therefore, at least N subcarriers are needed to feedback a singular vector. That is, the transmit covariance matrix, which is represented by a matrix R 120, can be decomposed using a singular value decomposition (SVD) asR=UΣVH,where U, V are the left and right singular vector matrices with N×N entries, and Σ is an N×N diagonal matrix whose entries are the singular values.
A largest singular vector 110, i.e., the column of the matrix V with a maximum magnitude, is feedback to the BS. The components of the largest singular vector {V1, V2, . . . , VN} are assigned to N subcarriers associated with N antennas. The complex numbers in the vector can be mapped to N subcarriers using, for example, amplitude modulation (AM).
Repetition 130 can be used to improve reliability in a low SNR range. Increasing the number of BS antennas improves performance on the UL. In a BS with 4 or 8 antennas, no repetition is required for most SNR ranges. Throughout this description, we use the notation Vmax, to denote the largest (maximum magnitude) singular vector.
It is possible to feedback only N−1 complex numbers by rotating all elements by a negative of an angle of the first element. This makes the first element real, so that the first element does not need to be transmitted.
If the angle of the vector V1 is φ, then the feedback is{exp(−jφ)*v2, . . . , exp(−jφ)*vN}, for j=1 to N.
At the BS, the first element can be determined because the sum power of all elements is 1. However, this makes the feedback more sensitive to power normalizations.
Because feedback in cellular networks, and in particular networks according to the IEEE 802.16m standard, is done per band (that is over 1 to 4 Physical Resource Blocks (PRB)). Two possibilities provide good results. Determine the largest singular vector of the average transmit covariance matrix in that band. Computation of the transmit covariance matrix is simple and needed for the adaptive mode.
General computation of the largest singular vector can be facilitated in most cases using a power method, or via the general SVD.
In most cases, the mobile stations have two receive antennas. Therefore, a simple closed form formula for the SVD of each subcarrier channel, for any number N of BS antennas, can be determined. It is also possible to average the singular vectors in a given band.
In particular for rank-1 feedback, the largest singular vector is simply a linear combination of the two channel rows, and the singular vectors are phase aligned before being averaged across the band of interest. A second averaging iteration can improve performance.
For MS with four antennas, a maximum likelihood (ML) receiver can be used for spatial multiplexing. An implementation can use a sphere decoder. The sphere decoders performs a QR decomposition to construct a search tree. After the QR decomposition is performed, obtaining the SVD is just another stage of the same procedure.